Nonparametric Treatment Effect Identification in School Choice

We study nonparametric identification and estimation of causal effects in centralized school assignment. We characterize the full set of identified treatment effects in common school choice settings, under unrestricted heterogeneity in individual potential outcomes. This exercise highlights two points of caution for practitioners: We find that lack of overlap poses a challenge to regression-based estimators; we also find that, asymptotically, regression-based estimators that aggregate across many treatment contrasts put zero weight on treatment effects identified from regression-discontinuity (RD) variation, when the mechanism allows for both RD and lottery-based variation. Due to the complex interplay between heterogeneous causal effects and school choice algorithms, we recommend empirical researchers clearly decompose aggregate causal effect estimates by sources of variation in these settings. Lastly, we provide estimators and accompanying asymptotic results for causal contrasts identified by RD variation in school choice.
Presented at SOLE 2021